Galactic Emperor

 isn't really one of the mini Bosses, but is hard enough to be considered one that you face in the Story Missions of Battleborn.

Strategy
The Galactic Emperor isn't really considered a Boss, but I found him to be pretty much harder to deal with than the other "Bosses". You'll need to deal damage to him quickly since he'll drop down and heal while he summons 3 micro copies of himself, which is a pain if you're not aware that he can heal from basically no health to full if you're taking your time. Destroy the frozen shield and take him out ASAP.